Finite Group Databasebeta

← #14769174

Subgroups — #14769174

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623140C211yesmaximal, characteristic
2C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4C2×D11×#102C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069420C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13068934C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068546C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1893C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66990—21no—
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C22×C8×D11C2211yescharacteristic, complemented
26#10623140—24no—
27#10623140C418yescomplemented
28C2×#66948C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic, complemented
31C2×#66937—21no—
32C2×#66935—21no—
33C2×(C22⋊D11)⋊C4—21no—
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×#102C2211yescharacteristic, complemented
36C11×#380C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38C2×#66896C2211yescharacteristic, complemented
39C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
40C2×#66885—24no—
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic, complemented
44C2×#66885C2211yescharacteristic, complemented
45C8×C22⋊D11—24no—
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48C2×C8×Dic11C2211yescharacteristic, complemented
49#10622600C2211yescharacteristic, complemented
50#10622589C2211yescharacteristic, complemented
51C4⋊C4×Dic11C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic, complemented
55C2×#66873C2211yescharacteristic, complemented
56#10622559—21no—
57D11×#102—24no—
58#10622281—21no—
59#10622260—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×C22⋊D11D411yescharacteristic
73C23×Dic11—21no—
74C2×D4×D11—28no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—41no—
79C2×D4×D11—41no—
80C2×D4×D11—44no—
81C2×D4×D11—44no—
82C2×D4×D11C2×C414yescomplemented
83C22×D44—22no—
84C22×D44—22no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44—22no—
88C22×D44—41no—
89C22×D44—41no—
90C22×D44C2×C414yescomplemented
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11—21no—
95C22×C4×D11C2311yescharacteristic
96C22×C8×C11—22no—
97C22×C8×C11—22no—
98C22×C8×C11—41no—
99C22×C8×C11C2311yescharacteristic
100C22×C8×C11C2311yescharacteristic
101C11×#121—22no—
102C11×#121C2×C414yescomplemented
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4—21no—
108C2×C22⋊Dic11D411yescharacteristic
109#66993—22no—
110#66993C2×C414yescomplemented
111#66990—28no—
112C4×C22⋊D11C2×C414yes—
113C4×C22⋊D11D414yes—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4D411yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C2×C8×D11—22no—
132C2×C8×D11—22no—
133C2×C8×D11—41no—
134#66948—22no—
135#66948C2×C414yescomplemented
136#66946—22no—
137#66946C2×C414yescomplemented
138C4⋊C4×D11—22no—
139C4⋊C4×D11—41no—
140#66937—28no—
141#66935—28no—
142(C22⋊D11)⋊C4—44no—
143C11×#102—22no—
144C11×#102—41no—
145C11×#95—21no—
146#66896—22no—
147#66896—41no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C22⋊(C11⋊C8)—22no—
151#66885—22no—
152#66885—22no—
153#66885—22no—
154#66885D414yescomplemented
155(C2×D11)⋊C8—22no—
156Dic11⋊C8—22no—
157C8×Dic11—22no—
158#66873—22no—
159#66873—22no—
160#66873—41no—
161#66873—41no—
162D4×#102—111nomaximal, Sylow
163C24×C11—21no—
164C24×C11C2×D411yescharacteristic
165C23×D11—21no—
166C23×D11—21no—
167C23×D11—24no—
168C23×D11—24no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11—42no—
176C23×D11—42no—
177C23×D11—81no—
178C23×D11—81no—
179C23×D11—81no—
180C23×D11—81no—
181C23×D11C2×D411yescharacteristic
182C2×D4×C11—24no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—21no—
188C2×D4×C11—42no—
189C2×D4×C11—42no—
190C2×D4×C11C22×C412yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—81no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11C22⋊C414yes—
212C2×C22⋊D11D814yes—
213C2×C22⋊D11SD1614yes—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11—81no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222D4×D11—28no—
223D4×D11—44no—
224D4×D11—44no—
225D4×D11—44no—
226D4×D11—432no—
227C2×D44—24no—
228C2×D44—28no—
229C2×D44—24no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—21no—
238C2×D44—42no—
239C2×D44—42no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—44no—
243C2×D44—42no—
244C2×D44—42no—
245C2×D44C22×C412yes—
246C2×D44C22×C412yes—
247C2×D44C2×D412yes—
248C2×D44#4112yes—
249C2×C4×D11—24no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—42no—
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C2×C4×D11—42no—
258C2×C4×D11—81no—
259C2×C4×D11C22×C412yes—
260C2×C4×D11C2×D412yes—
261C2×C8×C11—21no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—44no—
267C2×C8×C11C2×D412yescomplemented
268C11×C4⋊C4—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4C22×C412yes—
274C11×C22⋊C4—24no—
275C11×C22⋊C4—42no—
276C22⋊Dic11C22⋊C414yes—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—42no—
280(C2×D11)⋊C4C22⋊C414yes—
281C4⋊Dic11—21no—
282C4⋊Dic11—21no—
283C4⋊Dic11—21no—
284C4⋊Dic11—42no—
285C4⋊Dic11C2×D412yescomplemented
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288Dic11⋊C4—81no—
289Dic11⋊C4C22⋊C414yes—
290C4×Dic11—42no—
291C4×Dic11C22×C412yes—
292C4×Dic11C2×D412yes—
293C2×C11⋊C8—21no—
294C2×C11⋊C8—21no—
295C2×C11⋊C8—21no—
296C2×C11⋊C8—21no—
297C2×C11⋊C8—21no—
298C2×C11⋊C8—21no—
299C8×D11—44no—
300C2×D42—111no—
301C2×C8×D4—111no—
302C22×#102—111no—
303C22×#102—111no—
304D4×C4⋊C4—111no—
305#1982—111no—
306#1957—111no—
307#1893—111no—
308#1893D1111yescharacteristic, complemented
309#1874—111no—
310#1874—111no—
311#1802—111no—
312#1786—111no—
313#1786—111no—
314C4×#102—111no—
315C23×C11—21no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—22no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11C2×C22⋊C412yes—
327C23×C11C2×D812yes—
328C23×C11C2×SD1612yes—
329C23×C11C22×D411yescharacteristic
330C22×D11—21no—
331C22×D11—21no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—48no—
339C22×D11—48no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—48no—
351C22×D11—48no—
352C22×D11—84no—
353C22×D11—84no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11—84no—
360C22×D11—84no—
361C22×D11—84no—
362C22×D11C2×C22⋊C412yes—
363C22×D11C2×D812yes—
364C22×D11C2×SD1612yes—
365D4×C11—22no—
366D4×C11—22no—
367D4×C11—48no—
368D4×C11—41no—
369D4×C11—41no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11C2×C22⋊C412yes—
386C2×C4×C11C23×C411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C22×D411yescharacteristic
389C2×C4×C11C2×#4111yescharacteristic
390C2×C4×C11H(5,𝔽2)11yescharacteristic
391C2×C4×C11H(5,𝔽2)11yescharacteristic
392C22⋊D11—48no—
393C22⋊D11—48no—
394C22⋊D11—84no—
395C22⋊D11#102116yescomplemented
396C2×Dic11—21no—
397C2×Dic11—21no—
398C2×Dic11—21no—
399C2×Dic11—21no—
400C2×Dic11—22no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—84no—
407C2×Dic11C2×C22⋊C412yes—
408C2×Dic11C2×C22⋊C412yes—
409C2×Dic11C2×C22⋊C412yes—
410C2×Dic11C2×D812yes—
411C2×Dic11C2×SD1612yes—
412D44—22no—
413D44—22no—
414D44—22no—
415D44—22no—
416D44—22no—
417D44—48no—
418D44—48no—
419D44—41no—
420D44—41no—
421D44C4×D414yescomplemented
422C4×D11—22no—
423C4×D11—22no—
424C4×D11—22no—
425C4×D11—22no—
426C4×D11—48no—
427C4×D11—84no—
428C8×C11—22no—
429C8×C11—41no—
430C11⋊C8—41no—
431C11⋊C8—41no—
432C23×D4—111no—
433C23×D4—111no—
434C23×D4—221no—
435C23×C8—111no—
436C23×C8C2×D1111yescharacteristic, complemented
437D42—118no—
438D42—224no—
439C2×#127—111no—
440C2×#121—111no—
441C2×#121—221no—
442C2×#121C2×D1111yescharacteristic
443C2×#120—221no—
444C2×#120—221no—
445C2×C4×D4—111no—
446C2×C4×D4—111no—
447C2×C4×D4—221no—
448C22×C4⋊C4—111no—
449C22×C4⋊C4—111no—
450C8×D4—224no—
451C2×C4⋊C8—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459C2×#102—111no—
460C2×#102—111no—
461C2×#102—111no—
462C2×#102—224no—
463C2×#102—224no—
464C2×#102C2×D1111yescharacteristic, complemented
465C2×#102C2×D1111yescharacteristic, complemented
466C2×C22⋊C8—111no—
467C2×C22⋊C8—111no—
468C2×C4×C8—111no—
469#389—221no—
470#385—221no—
471#385—221no—
472#384—111no—
473#380—111no—
474#380C2×D1111yescharacteristic, complemented
475C4×C4⋊C4—111no—
476#340—111no—
477#340—111no—
478#340C2×D1111yescharacteristic, complemented
479#340C2×D1111yescharacteristic, complemented
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—81no—
490C22×C11—81no—
491C22×C11—81no—
492C22×C11—81no—
493C22×C11C2×#10214yescomplemented
494C22×C11C22×C22⋊C411yescharacteristic
495C22×C11D4211yescharacteristic
496C22×C11#54611yescharacteristic
497C22×C11C22×D811yescharacteristic
498C22×C11C22×SD1611yescharacteristic
499C22×C11#57611yescharacteristic
500C22×C11#57711yescharacteristic
501C2×D11—22no—
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—22no—
506C2×D11—22no—
507C2×D11—24no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—816no—
518C2×D11—816no—
519C2×D11—81no—
520C2×D11—81no—
521C2×D11—81no—
522C2×D11—81no—
523C2×D11C2×#10214yescomplemented
524C4×C11—22no—
525C4×C11—42no—
526C4×C11—81no—
527C4×C11—81no—
528C4×C11C2×C4×D411yescharacteristic
529C4×C11#51811yescharacteristic
530C4×C11D4211yescharacteristic
531C4×C11#54611yescharacteristic
532Dic11—22no—
533Dic11—22no—
534Dic11—42no—
535Dic11—81no—
536Dic11C2×#10214yescomplemented
537C25—221no—
538C25—221no—
539C22×D4—21no—
540C22×D4—111no—
541C22×D4—114no—
542C22×D4—114no—
543C22×D4—111no—
544C22×D4—111no—
545C22×D4—222no—
546C22×D4—222no—
547C22×D4—221no—
548C22×D4—222no—
549C22×D4—221no—
550C22×D4—221no—
551C22×D4—221no—
552C22×D4—222no—
553C22×D4—222no—
554C22×D4—228no—
555C22×D4—221no—
556C22×D4—222no—
557C22×D4—441no—
558C22×D4—441no—
559C22×D4—441no—
560C22×D4—441no—
561C22×D4—444no—
562C22×D4—444no—
563C22×D4C22×D1111yescharacteristic
564C23×C4—111no—
565C23×C4—221no—
566C23×C4—221no—
567C23×C4—221no—
568C23×C4C22×D1111yescharacteristic
569C22×C8—22no—
570C22×C8—22no—
571C22×C8—41no—
572C22×C8—111no—
573C22×C8—111no—
574C22×C8—222no—
575C22×C8—222no—
576C22×C8—441no—
577C22×C8C22×D1111yescharacteristic
578C22×C8C22×D1111yescharacteristic
579#127—114no—
580#127—222no—
581#121—22no—
582#121—114no—
583#121—228no—
584#121—222no—
585#121C4×D1114yescomplemented
586#120—228no—
587#120—228no—
588C4×D4—114no—
589C4×D4—114no—
590C4×D4—114no—
591C4×D4—222no—
592C4×D4—444no—
593C2×C4⋊C4—111no—
594C2×C4⋊C4—111no—
595C2×C4⋊C4—111no—
596C2×C4⋊C4—222no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—441no—
603C2×C4⋊C4—441no—
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C4⋊C4C22×D1111yescharacteristic
606C2×C4⋊C4C22×D1111yescharacteristic
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—111no—
610C2×C22⋊C4—111no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C42—111no—
615C2×C42—221no—
616C4⋊C8—222no—
617#102—22no—
618#102—41no—
619#102—114no—
620#102—222no—
621#102—222no—
622#102—222no—
623#102—222no—
624#102—222no—
625#102—222no—
626#102—441no—
627#102—441no—
628#102—441no—
629C22⋊C8—222no—
630C22⋊C8—222no—
631C4×C8—222no—
632#95—21no—
633#95—221no—
634#95—221no—
635C2×C11—24no—
636C2×C11—82no—
637C2×C11D4×C22⋊C411yescharacteristic
638C2×C11C22×#10211yescharacteristic
639C2×C11#289711yescharacteristic
640C2×C11D4×D811yescharacteristic
641C2×C11D4×SD1611yescharacteristic
642C2×C11#329411yescharacteristic
643C2×C11#329511yescharacteristic
644D11—24no—
645D11—44no—
646D11—82no—
647C24—21no—
648C24—111no—
649C24—224no—
650C24—221no—
651C24—221no—
652C24—224no—
653C24—442no—
654C24—442no—
655C24—442no—
656C24—442no—
657C24—442no—
658C24—442no—
659C24—442no—
660C24—442no—
661C24—881no—
662C24—881no—
663C24—881no—
664C24—881no—
665C24D4×D1111yescharacteristic
666C2×D4—24no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—114no—
675C2×D4—114no—
676C2×D4—114no—
677C2×D4—112no—
678C2×D4—112no—
679C2×D4—112no—
680C2×D4—112no—
681C2×D4—228no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—224no—
686C2×D4—228no—
687C2×D4—224no—
688C2×D4—221no—
689C2×D4—221no—
690C2×D4—221no—
691C2×D4—221no—
692C2×D4—221no—
693C2×D4—221no—
694C2×D4—221no—
695C2×D4—221no—
696C2×D4—444no—
697C2×D4—444no—
698C2×D4—444no—
699C2×D4—442no—
700C2×D4—442no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—442no—
704C2×D4—442no—
705C2×D4—444no—
706C2×D4—444no—
707C2×D4—444no—
708C2×D4—442no—
709C2×D4—442no—
710C2×D4—4432no—
711C2×D4—881no—
712C2×D4—881no—
713C2×D4C2×C4×D1112yes—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—111no—
722C22×C4—111no—
723C22×C4—111no—
724C22×C4—112no—
725C22×C4—112no—
726C22×C4—224no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—442no—
734C22×C4—442no—
735C22×C4—442no—
736C22×C4—442no—
737C22×C4—442no—
738C22×C4—442no—
739C22×C4—881no—
740C22×C4—881no—
741C22×C4C2×C4×D1112yes—
742C22×C4D4×D1111yescharacteristic
743C22×C4D4×D1112yes—
744C22×C4C23×D1111yescharacteristic
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8—221no—
752C2×C8—221no—
753C2×C8—221no—
754C2×C8—221no—
755C2×C8—221no—
756C2×C8—221no—
757C2×C8—444no—
758C2×C8D4×D1112yescomplemented
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—114no—
765C4⋊C4—112no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C4⋊C4—221no—
769C4⋊C4—442no—
770C4⋊C4—442no—
771C4⋊C4—442no—
772C4⋊C4—881no—
773C4⋊C4C2×C4×D1112yes—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—114no—
777C22⋊C4—114no—
778C22⋊C4—224no—
779C22⋊C4—224no—
780C22⋊C4—442no—
781C42—112no—
782C42—112no—
783C42—442no—
784C11D4×#10211yescharacteristic, complemented, Sylow
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—112no—
797C23—112no—
798C23—112no—
799C23—221no—
800C23—221no—
801C23—221no—
802C23—221no—
803C23—222no—
804C23—222no—
805C23—222no—
806C23—222no—
807C23—448no—
808C23—448no—
809C23—448no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—441no—
817C23—441no—
818C23—441no—
819C23—441no—
820C23—448no—
821C23—884no—
822C23—884no—
823C23—884no—
824C23—884no—
825C23—884no—
826C23—884no—
827C23—884no—
828C23—884no—
829C23—884no—
830C23—884no—
831C23C22⋊C4×D1112yes—
832C23D8×D1112yes—
833C23SD16×D1112yes—
834C23C2×D4×D1111yescharacteristic
835D4—22no—
836D4—22no—
837D4—48no—
838D4—41no—
839D4—41no—
840D4—1116no—
841D4—114no—
842D4—222no—
843D4—222no—
844D4—222no—
845D4—222no—
846D4—222no—
847D4—448no—
848D4—448no—
849D4—448no—
850D4—448no—
851D4—441no—
852D4—441no—
853D4—884no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—112no—
870C2×C4—112no—
871C2×C4—112no—
872C2×C4—112no—
873C2×C4—112no—
874C2×C4—221no—
875C2×C4—221no—
876C2×C4—221no—
877C2×C4—221no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—448no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—884no—
890C2×C4—884no—
891C2×C4C22⋊C4×D1112yes—
892C2×C4C22×C4×D1111yescharacteristic
893C2×C4C2×D4×D1111yescharacteristic
894C2×C4C2×D4×D1111yescharacteristic
895C2×C4#6703711yescharacteristic
896C2×C4#41×D1111yescharacteristic
897C2×C4#6704211yescharacteristic
898C8—22no—
899C8—41no—
900C8—441no—
901C8—441no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—114no—
916C22—222no—
917C22—222no—
918C22—222no—
919C22—222no—
920C22—222no—
921C22—222no—
922C22—224no—
923C22—442no—
924C22—442no—
925C22—442no—
926C22—442no—
927C22—442no—
928C22—442no—
929C22—442no—
930C22—442no—
931C22—442no—
932C22—8816no—
933C22—8816no—
934C22—881no—
935C22—881no—
936C22—881no—
937C22—881no—
938C22D11×#10214yescomplemented
939C22C2×C22⋊C4×D1111yescharacteristic
940C22#1062314011yescharacteristic
941C22#1062314111yescharacteristic
942C22C2×D8×D1111yescharacteristic
943C22C2×SD16×D1111yescharacteristic
944C22#1062330011yescharacteristic
945C22#1062330111yescharacteristic
946C4—22no—
947C4—42no—
948C4—81no—
949C4—81no—
950C4—114no—
951C4—222no—
952C4—222no—
953C4—442no—
954C4—881no—
955C4C4×D4×D1111yescharacteristic
956C4#1062307611yescharacteristic
957C4#1062312111yescharacteristic
958C4#1062318511yescharacteristic
959C2—24no—
960C2—82no—
961C2—224no—
962C2—444no—
963C2—882no—
964C2#1307143411yescharacteristic
965C2C2×D11×#10211yescharacteristic
966C2#1307713811yescharacteristic
967C2#1308029011yescharacteristic
968C2#1308030911yescharacteristic
969C2#1308042411yescharacteristic
970C2#1308043511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1893C2
socleC23×C11C22×D4
prime radicalC2×#10623140C2
cosocleC22×C4×C11C24
hypercenter#1893D11
hypocenterC11D4×#102
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C8×C22⋊D11C2semidirect
3. C22×#66885C2semidirect
4. C2×D11×#102C2semidirect
5. #13071512C2semidirect
6. #13069541C2semidirect
7. #13069420C2semidirect
8. #13069043C2semidirect
9. #13068934C2semidirect
10. #13068932C2semidirect
11. #13068615C2semidirect
12. #13068546C2semidirect
13. #13068545C2semidirect
14. #13068430C2semidirect
15. C11×#1893C2semidirect
19. C23×C8×C11C22semidirect
24. C22×C4⋊Dic11C22semidirect
25. C22×C8×D11C22semidirect
27. #10623140C4semidirect
30. C2×C4⋊C4×D11C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×#102C22semidirect
36. C11×#380C22semidirect
37. C2×#66896C22semidirect
38. C2×#66896C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
43. C2×#66885C22semidirect
44. C2×#66885C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
47. C2×Dic11⋊C8C22semidirect
48. C2×C8×Dic11C22semidirect
49. #10622600C22semidirect
50. #10622589C22semidirect
51. C4⋊C4×Dic11C22semidirect
54. C2×#66873C22semidirect
55. C2×#66873C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
82. C2×D4×D11C2×C4semidirect
90. C22×D44C2×C4semidirect
102. C11×#121C2×C4semidirect
110. #66993C2×C4semidirect
135. #66948C2×C4semidirect
137. #66946C2×C4semidirect
154. #66885D4semidirect
267. C2×C8×C11C2×D4semidirect
285. C4⋊Dic11C2×D4semidirect
308. #1893D11semidirect
395. C22⋊D11#102semidirect
421. D44C4×D4semidirect
436. C23×C8C2×D11semidirect
464. C2×#102C2×D11semidirect
465. C2×#102C2×D11semidirect
474. #380C2×D11semidirect
478. #340C2×D11semidirect
479. #340C2×D11semidirect
493. C22×C11C2×#102semidirect
523. C2×D11C2×#102semidirect
536. Dic11C2×#102semidirect
585. #121C4×D11semidirect
758. C2×C8D4×D11semidirect
784. C11D4×#102semidirect
938. C22D11×#102semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106231402
C2×C8×C22⋊D112
C22×#668852
C2×D11×#1022
#130715122
#130695412
#130694202
#130690432
#130689342
#130689322
#130686152
#130685462
#130685452
#130684302
C11×#18932
D4×#10211